On the characterization of some families of closed convex sets
type: Item
instance of: scholarly article
title: On the characterization of some families of closed convex sets
zbMATH Open document ID: 1009.52008
published in: Beiträge zur Algebra und Geometrie
publication date: 2002-08-20T00:00:00Z
full work available at URL: https://eudml.org/doc/228025
full work available at URL: 12.html
review text: The authors obtain characterizations of simplices, sandwiches (convex hulls of pairs of parallel affine manifolds), parallelotopes and sums of compact convex sets with linear subspaces in terms of their internal and conical representations. They also provide characterizations of some of these interesting families of sets using visibility properties of their boundary points and prove that a closed convex set is a sandwich if and only if its relative boundary is not connected. Applications of some of these characterizations are also studied and it is proved that a bounded linear semi-infinite programming problem whose feasible set is the sum of a compact convex set with a linear subspace is necessarily solvable and has zero duality gap.
Mathematics Subject Classification ID: 52A20
Mathematics Subject Classification ID: 90C34
Mathematics Subject Classification ID: 52A41
Mathematics Subject Classification ID: 52A40
zbMATH DE Number: 1784599
zbMATH Keywords: closed convex sets
zbMATH Keywords: simplices
zbMATH Keywords: sandwiches
zbMATH Keywords: parallelotopes
zbMATH Keywords: linear inequalities
zbMATH Keywords: connectivity
zbMATH Keywords: visibility
zbMATH Keywords: linear semi-infinite programming
zbMATH Keywords: feasible set
author: Miguel Angel Goberna
author: Valentín Jornet
author: Margarita M. L. Rodríguez
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1784599